Higgs boson mass in NMSSM with right-handed neutrino

In order to have massive neutrinos, the right-handed neutrino/sneutrino superfield ($N$) need to be introduced in supersymmetry. In the framework of NMSSM (the MSSM with a singlet $S$) such an extension will dynamically lead to a TeV-scale Majorana mass for the right-handed neutrino through the $SNN$ coupling when $S$ develops a vev (the free Majorana mass term is forbidden by the assumed $Z_3$ symmetry). Also, through the couplings $SNN$ and $SH_uH_d$, the SM-like Higgs boson (a mixture of $H_u$, $H_d$ and $S$) can naturally couple with the right-handed neutrino/sneutrino. As a result, the TeV-scale right-handed neutrino/sneutrino may significantly contribute to the Higgs boson mass. Through an explicit calculation, we find that the Higgs boson mass can indeed be sizably altered by the right-handed neutrino/sneutrino. Such new contribution can help to push up the SM-like Higgs boson mass and thus make the NMSSM more natural.